NumXL Support Desk

Appendix A: Likelihood function (LLF)

The likelihood function (aka likelihood/LLF) is a function of the parameters of a statistical model. In other words, the likelihood of model parameters given some observed outcome (i.e. sample) is equal to the probability of those outcomes given the model and its parameters values.

In non-technical parlance, "likelihood" is usually a synonym for "probability" but in statistical usage, a clear technical distinction is made.

For many applications involving likelihood functions, it is more convenient to work in terms of the natural logarithm of the likelihood function, called the log-likelihood, than in terms of the likelihood function itself. Because the logarithm is a monotonically increasing function, the logarithm of a function achieves its maximum value at the same points as the function itself, and hence the log-likelihood can be used in place of the likelihood in maximum likelihood estimation and related techniques.

By definition, the likelihood function for a statistical model is described as: